Universal meager F σ -sets in locally compact manifolds

Taras O. Banakh; Dušan Repovš

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 2, page 179-188
  • ISSN: 0010-2628

Abstract

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In each manifold M modeled on a finite or infinite dimensional cube [ 0 , 1 ] n , n ≤ ω , we construct a meager F σ -subset X ⊂ M which is universal meager in the sense that for each meager subset A ⊂ M there is a homeomorphism h : M → M such that h ( A ) ⊂ X . We also prove that any two universal meager F σ -sets in M are ambiently homeomorphic.

How to cite

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Banakh, Taras O., and Repovš, Dušan. "Universal meager $F_\sigma $-sets in locally compact manifolds." Commentationes Mathematicae Universitatis Carolinae 54.2 (2013): 179-188. <http://eudml.org/doc/252474>.

@article{Banakh2013,
abstract = {In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$, $n\le \omega $, we construct a meager $F_\sigma $-subset $X\subset M$ which is universal meager in the sense that for each meager subset $A\subset M$ there is a homeomorphism $h:M\rightarrow M$ such that $h(A)\subset X$. We also prove that any two universal meager $F_\sigma $-sets in $M$ are ambiently homeomorphic.},
author = {Banakh, Taras O., Repovš, Dušan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {universal nowhere dense subset; Sierpiński carpet; Menger cube; Hilbert cube manifold; $n$-manifold; tame ball; tame decomposition; universal nowhere dense subset; Sierpiński carpet; Menger cube; Hilbert cube manifold; tame ball; tame decomposition},
language = {eng},
number = {2},
pages = {179-188},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Universal meager $F_\sigma $-sets in locally compact manifolds},
url = {http://eudml.org/doc/252474},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Banakh, Taras O.
AU - Repovš, Dušan
TI - Universal meager $F_\sigma $-sets in locally compact manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 2
SP - 179
EP - 188
AB - In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$, $n\le \omega $, we construct a meager $F_\sigma $-subset $X\subset M$ which is universal meager in the sense that for each meager subset $A\subset M$ there is a homeomorphism $h:M\rightarrow M$ such that $h(A)\subset X$. We also prove that any two universal meager $F_\sigma $-sets in $M$ are ambiently homeomorphic.
LA - eng
KW - universal nowhere dense subset; Sierpiński carpet; Menger cube; Hilbert cube manifold; $n$-manifold; tame ball; tame decomposition; universal nowhere dense subset; Sierpiński carpet; Menger cube; Hilbert cube manifold; tame ball; tame decomposition
UR - http://eudml.org/doc/252474
ER -

References

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  2. Banakh T., Morayne M., Rałowski R., Żeberski S., Topologically invariant σ -ideals on the Hilbert cube, preprint (http://arxiv.org/abs/1302.5658). 
  3. Banakh T., Repovš D., Universal nowhere dense subsets of locally compact manifolds, preprint (http://arxiv.org/abs/1302.5651). 
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